Former New York Times executive editor Jill Abramson wrote in her debut as a Guardian columnist on Tuesday that Hillary Clinton is a “fundamentally honest and trustworthy” person. Poll after poll indicates voters disagree — in a Washington Post-ABC News survey this month, 57 percent said she isn’t — but Abramson makes a good case.

It was bad judgment, as [Clinton] has said, to use a private email server. It was colossally stupid to take those hefty speaking fees, but not corrupt. There are no instances I know of where Clinton was doing the bidding of a donor or benefactor.

As for her statements on issues, Politifact, a Pulitzer prize-winning fact-checking organization, gives Clinton the best truth-telling record of any of the 2016 presidential candidates.

If we imagine, for a moment, that the news media could generally accept Abramson’s argument, the question that follows is: How would coverage of Clinton change?

The answer, I suspect, is not a whole lot.

Clinton’s problem, according to Abramson, isn’t so much that she doesn’t tell the truth; it’s that she isn’t transparent. When something looks a little shady — like, say, those speaking fees from Goldman Sachs — Clinton’s natural response is defensiveness, rather than disclosure. She doesn’t think she should have to release transcripts of her remarks to prove there was no quid pro quo; she thinks journalists and voters should take her at her word (and also get off her back because, hey, $675,000 for three speeches is “what they offered”).

Sorry, but that’s not how it works. The great investigative reporter Walter Robinson (you might know him as Michael Keaton’s character in “Spotlight”) often quoted Ronald Reagan when I was a graduate student of his at Northeastern University: “Trust but verify.”

This is how journalists should operate, Robby said. They shouldn’t be so cynical as to distrust every claim by the people they cover, but they should also demand evidence.

Clinton makes the verification process difficult. From a media perspective, that’s a big piece of her email scandal. National security concerns are paramount, of course, but for journalists, it’s hard to shake the feeling that Clinton conducted official business on a private account so that her correspondence wouldn’t be subject to public records requests.

Clinton’s private email usage became a big story last year after a front-page article in the New York Times; often forgotten, however, is Gawker’s report on the practice in 2013, which noted “there seems to be little reason to use a different account other than an attempt to shield her communications … from the prying eyes of FOIA requesters.” Gawker made a Freedom of Information Act request for emails between Clinton and an adviser and was informed by the State Department that none were on file. Not cool.

Even if there was nothing scandalous in the emails — even if Clinton really is “fundamentally honest and trustworthy” — journalists are understandably suspicious when a politician appears to be trying to hide something.

What’s more, the fact that so many voters view Clinton as untrustworthy makes her perceived dishonesty a legitimate campaign issue. Perceptions in politics are sometimes wrong — John Edwards was once viewed as the consummate family man — and it is the job of the press to find the truth, not simply reinforce what voters already believe. But any comprehensive analysis of the horse race has to account for what people think about the candidates’ character.

So maybe Abramson is right about Clinton. But until the Democratic front-runner opens up a bit, it’s going to be hard for her to change voters’ minds — or the way the media cover her.